a. Field of the Invention
The present invention relates generally to methods for the analysis of two-dimensional images, and, more particularly, to a method for analyzing two-dimensional images by using gray-scale density variations of the image to calculate a third axis which is used to produce a virtual 3-dimensional image for quantitative and qualitative analysis.
b. Background Art
There are many instances in which it is desirable to analyze a two-dimensional image in order to ascertain certain characteristics or qualities relating to the image. For example, it is often necessary to analyze and compare handwriting samples in order to determine the authenticity of a signature or other writing. Similarly, fingerprints, ballistics patterns and DNA patterns (xe2x80x9csmearsxe2x80x9d) require analysis and comparison in order to match them to an individual or a weapon. Still further, outside the fields of criminology and forensics, many medical and industrial processes and tests require analysis of two-dimensional images, such as analysis of the fine details of image density depicted on medical x-rays and MRI""s, for example.
These are just a few examples of the vast array of two-dimensional images that may require analysis and comparison. Therefore, although the following discussion focuses largely on analysis of handwriting for the purpose of illustrating a preferred embodiment of the present invention, it will be understood that the scope of the present invention includes analysis of all two-dimensional images that are susceptible to the methods described herein.
Conventional methods for analyzing two-dimensional images are generally labor-intensive, subjective, and highly dependent on the individual analyst""s experience and attention to detail. Not only do these factors increase the cost of the process, but they also tend to introduce inaccuracies that reduce the value of the results. The analysis of handwriting particularly illustrates these problems. Sometimes referred to as graphoanalysis, or questioned document examination (QDE), handwriting analysis is most commonly conducted for purpose of determining the authenticity of a document or signature. In some instances, however, handwriting analysis may be conducted for other reasons, such as for comparing a person""s writing against predetermined criteria to determine aspects of the writer""s personality or emotional characteristics; for example, handwriting is often analyzed for the purpose for evaluating a person""s emotional responsiveness and their suitability for employment in a position requiring particular skills or traits, or for assignment to work with certain groups of people or to perform certain tasks.
Analyzing handwriting for any of these purposes involves obtaining numerous, painstaking measurements from one or more samples of the writing. For example, to determine whether or not a particular person wrote a certain document, minute details of the writing must be measured, catalogued and compared to measurements taken from a sample of known authenticity, much in the manner of fingerprint analysis. Similarly, to determine a writer""s emotional characteristics from a handwriting sample, a great many measurements of heights, angles and other features are taken from individual letters and words throughout the writing, and these measurements are then analyzed statistically and compared with certain predetermined standards, which themselves have been produced by compiling a vast number of measurements taken from handwriting produced by persons having known emotional characteristics.
Although the value of handwriting analysis is well recognized, its widespread use has been hampered by the fact that the necessary measurements have in the past been obtained almost invariably by manual means, using a magnifying glass, or protractor, pencil and other unsophisticated tools. Because of the sheer number of measurements involved, analyzing even a single person""s handwriting has thus been a time-consuming and expensive process. Moreover, since manual measurement techniques involve drawing various lines and marks on the sample using a pencil or other writing instrument, these techniques necessarily deface/damage the original to some extent, which renders subsequent measurements even more difficult and decreases the usefulness of original document.
Perhaps an even more serious problem is the degree of inaccuracy which is inherent in such manual techniques. Human judgment and therefore human error are inevitably present in such techniques, and consequently accuracy is heavily dependent on the manual dexterity and skills of the individual analyst. Furthermore, since analyzing even a single handwriting sample can involve taking hundreds of measurements, fatigue often becomes a very real factor and can impair the efforts of even the most skilled practitioner. Still further, many aspects of the process are quite subjective in nature, such determining the baselines and other starting points, and so there can be a high degree of variability between measurements taken from the same sample by different analysts.
Moreover, even when performed by a skilled analyst using the greatest degree of care, there are certain determinations that are virtually impossible to make when using conventional techniques. For example, a recurring question is whether a signature was applied to a document before or after it was printed. This is done by trying to determine whether the writing passes on top of the printing, or vice versa. Previously, there has existed no reliable way for making this determination, and it is very common for different analysts to come to completely different conclusions when examining the same document.
As a result, the inefficiencies and inaccuracies that are inherent in conventional handwriting analysis have limited its widespread availability and use. For example, graphoanalysis is potentially an extremely valuable tool for human resources departments and governmental agencies, but the problems with cost and accuracy have limited its adoption in these areas. Similarly, the difficulty in obtaining economical and accurate analysis of handwriting specimens has rendered this resource unavailable to many criminal and civil investigators, especially for police departments and other agencies located more rural areas, where availability of skilled handwriting analysts tends to be limited and budgets tend to be tight.
As was stated above, handwriting analysis is just one example of the many areas where improved methods for analysis of two-dimensional images are needed. Many of the same factors and problems discussed above apply with equal force to the analysis of two-dimensional images of other types and for different purposes. Many of these purposes lie within the field of criminology (DNA matching and ballistics analysis, for example), but, as was noted above, many other instances occur in industry, science and other fields of endeavor.
Accordingly, there exists a need for a method for conducting analysis of two-dimensional images, having variable color densities, proportional relationships or other characteristics which does not require measurements to be performed manually, and which therefore minimizes or eliminates the elements of inaccuracy and variability that are inherent in manual measurements. Furthermore, there exists a need for such a method that enables large numbers of measurements to be obtained, compiled and analyzed quickly and economically. Still farther, there exists a need for such a method that enables such measurements to be taken in a uniform manner, so that these can be compared with other samples or to predetermined standards in order to precisely and accurately identify internal consistencies. Still further, there exists a need for such a method, which will enable analysts to examine features of two-dimensional images that have not been visible or apparent when using conventional techniques. Still further, there exists a need for such a method which is easy and convenient to use, and which minimizes the physical and visual stress imposed on the operator in performing the analysis. Still farther, there exists a need for such a method which will permit measurements to be taken and used by a trained analyst who may be located remote from the site of the source image itself, so as to make this resource more readily available to persons and organizations in geographically remote areas.
The present invention has solved the problems cited above, and is a method for analysis of two-dimensional images having variable color densities, proportional relationships or other characteristics. Broadly, the method comprises the steps of: (a) measuring gray-scale densities at each of a plurality of locations having X-Y axis coordinates lying within the plane of the image; (b) calculating a value for each of the measured gray-scale densities so as to determine a z-axis coordinate for each of the locations; and (c) plotting the X-Y-Z axis coordinates for each of the locations so as to form a virtual 3-dimensional image having a contour that corresponds to variations in the gray-scale densities at the locations on the two-dimensional image.
The two-dimensional image may be a handwriting sample, or may be a two-dimensional image of a different type.
The step of measuring the gray-scale densities will comprise digitizing the two-dimensional image so as to form a digital bit map of the locations having the X-Y axis coordinates. The step of digitizing the two-dimensional image may comprise scanning the image so as to form the digital bit map.
The step of plotting the X-Y-Z axis coordinates for each of the locations may comprise forming the virtual three-dimensional image on a display monitor for visual analysis of the image by an operator. The step of forming the virtual three-dimensional image may comprise calculating the values for the measured gray-scale densities so as to provide Z-axis coordinates in a positive direction for each of the locations, so that the virtual three-dimensional image that is formed on the monitor appears as having raised contours. Alternatively, the values may be calculated so as to provide Z-axis coordinates in the negative direction for each of the locations, so that the virtual three-dimensional image appears as having depressed contours.
The method may further comprise the step of measuring at least one feature of the virtual three-dimensional image so as to analyze a characteristic of the two-dimensional image.
The step of measuring at least one feature of the virtual three-dimensional image may comprise measuring an apparent slope of the contours of the virtual three-dimensional image so as to analyze sharpness of an edge in the two-dimensional image.
The step of measuring at least one feature of the virtual three-dimensional image may comprise measuring apparent variations in elevation of the contours of the virtual three-dimensional image so as to analyze variations in color density in the two-dimensional image.
The step of measuring at least one feature of the virtual three-dimensional image may comprise measuring the apparent volume as defined by the contours of the three-dimensional image so as to analyze areas of relatively greater and lesser color density in the two-dimensional image. The step of measuring the apparent volume defined by the contours of the virtual three-dimensional image may comprise: selectively dividing the virtual three-dimensional image so as to define first and second portions of the image; measuring first and second apparent volumes defined by the contours of the first and second portions of the virtual three-dimensional image; and comparing the first and second apparent volumes so as to analyze distribution of the areas of greater and lesser color density in the two-dimensional image.
The two-dimensional image may be a stroke of writing in a handwriting sample, and the step of selectively dividing the virtual three-dimensional image may comprise: determining a maximum contour line extending generally lengthwise along the virtual three-dimensional image; dividing the virtual three-dimensional image along a plane extending from the maximum contour line in the direction of the Z-axis, so as to define the first and second portions of the image; measuring first and second volumes defined by the contours of the first and second portions of the virtual 3-dimensional image on opposite sides of the dividing plane; and comparing the first and second apparent volumes so as to analyze an angle in which a writing instrument was held as the stroke of writing was formed.
The present invention further provides a method for analysis of a handwriting sample, comprising the steps: (a) creating a digital representation of the handwriting sample; (b) marking at least first and second points on the digital representation which correspond to selected locations on the handwriting sample; and (c) comparing the first and second points on the digital representation so as to obtain a selective measurement of the handwriting sample.
The step of creating a visual representation of the handwriting sample may comprise forming a digital bit map of a plurality of locations having X-Y-axis coordinates lying within the plane of the handwriting sample. The step of marking of these first and second points on the digital representation may comprise marking at least first and second points on the digital bit map which correspond to selected locations on the handwriting sample.
The step of comparing the points marked on the bit map may comprise comparing the points so as to obtain a measurement of a slant angle of the handwriting sample.
The step of comparing the points on a bit map may comprise comparing the points so as to obtain a measurement of the height of the handwriting sample.
The step of marking the points on a bit map may comprise marking a plurality of points in a line which cuts across the selected stroke in the handwriting sample. The step of comparing the points so as to obtain a selected measurement may comprise measuring gray-scale density at the points in the line across the stroke; and translating the measured relative gray-scale density at the points so as to form a two-dimensional display for determining the angle of the writing instrument which formed the stroke.
The method may further comprise the steps of obtaining a plurality of the measurements for the handwriting sample, tabulating the plurality of measurements, and comparing the tabulated measurements with a predetermined standard so as to determine one or more characteristics relating to the person who produced the handwriting sample. The plurality of measurements may be compiled statistically to provide a unique identifier for the sample, and/or for the author or other originator of the sample.
The method may further comprise of the steps of measuring gray-scale densities at each of a plurality of locations having X-Y axis coordinates lying within the plane of the handwriting sample, calculating the value for each of the measured gray-scale densities so as to determine a Z-axis coordinate for each of the locations, and plotting the X-Y-Z axis coordinates for each of the locations so as to form a virtual three-dimensional image having a contour which corresponds to variations in the gray-scale densities at the locations on the handwriting sample.
These and other features and advantages of the present invention will be apparent from a reading of the following detailed description with reference to the accompanying drawings.